用Eviews软件建立一元线性回归模型并进行相关检验地实验报告材料

1、用Eviews软件建立一元线性回归模型并进行相关检验的实验报告1数据表1列出了某年中国部分省市城镇居民每个家庭平均全年可支配收入X与消费性支出Y地区可支配收入X消费性支出Y10349.698493.498140.506121.045661.164348.474724.113941.875129.053927.755357.794356.064810.004020.874912.883824.4411718.018868.196800.235323.189270.167020.226489.975022.004766.263830.715524.544644.506218.735218.7997

2、61.578016.915124.244276.674916.254126.475169.964185.735644.864422.93表12建立模型应用EViews软件，以表1的:可绘出可支配收入X与消费性支出Y的散点图（图2-1 X从该三点图可以看出，随着可支配收入的增加，消费性支出也在增加,大致程线性关系。据此,我们可以建立一性回归模型：Y=Po+PrX+p9.0003,0004,0008.000-7.000-6.000 _5000-4.000-6.0008.00010.000X12,000对模型作普通最小二乘法估计，在Eviews软件下，OLS的估计结果如图（2-2 ）所示。Depen

3、dent Variable: YMethod: Least SquaresDate: 12/07/11 Time: 21:00Sample: 1 20In eluded observations: 20VariableCoefficientStd. Errort-StatisticProb.X0.7553680.02327432.454860.0000C271.1197159.38001.7010900.1061R-squared0.983198Mean dependent var5199.515Adjusted R-squared 0.982265 S.D. dependent var162

4、5.275SE of regression216.4435Sum squared resid843260.4Log likelihood134.8718F-statistic1053.318Prob(F-statistic)0.000000Akaike info criterion13.68718Schwarz criterion13.78675HannanQuinn criter.13.70661Durbin-Watson stat1.302512图2-2OLS估计结果为r =271.12+0.76X(1.70) (32.45)R2=0.9832 D.W. =1.3025F=1053.318

5、3 模型检验从回归估计的结果看,模型拟合较好。可绝系数R2=0.983198 ,表明城镇居民每个家 庭平均全年消费性支出变化的98.3198%可由可支配收的变化来解释。从斜率项S的t检验 看，大于5%显著性水平下自由度为n-2=18的临界值to.o2s(18)=2.101 ,且该斜率值满足 0<0.755368<1 ,符合经济理论中边际消费倾向在0与之间的绝对收入假说，表明中国城 镇居民平均全年可支配收入每增加1元,消费性支出增加0.755368元。4 预测假设我们需要关注2012年平均年可支配收入在20000元这一水平下的中国城镇居民 平均年消费支出问题。由上述回归方程可得该类家

6、庭人均消费支出的预测值：丫0二 271.1197+0.755368x20000 二 15378.4797下面给出该类居民平均年消费支出95%置信度的预测区间。由于平均可支配收入X的样本均值与样本方差为E(X)=6222.209 Var(X) = 1994.033于是，在95%的置信度下，E(Yo)的预测区间为(874.28 , 16041.68)。而如果我们想知道某地区城镇居民年均可支配收入为20000元时,该居民消费支出的 个值预测，则仍为15378.4797。同样地,在95%的置信度下，该居民年均消费支出的预 测区间为(14581.14,16175.82 )。5异方差性检验对于经济发达地区

7、和经济落后地区，消费支出的决走因素不一走相同甚至差异很大，比 如经济越落后储蓄率反而会越高,可能就会出现异方差性的问题。(l)G-Q检验在对20个样本按X从大到小排序,去掉中间4个,对前后两个样本进行OLS估计, 样本容星为ni=n2=&前一个样本的OLS估计结果如图5-1所示。Dependent Variable: YMethod: Least SquaresDate: 12/07/11 Time: 22:21Sample: 1 8Included observations: 8VariableCoefficie ntStd.臼ror t-StatisticProb.X0.76214

8、10.06018712.662990.0000C210.9340529.39980.3984400.7041R-squared0.963932Mean dependent var6760.478Adjusted R-squared0.957920S.D. dependent var1556.814SE of regression319.3541Akaike info criterion14.58280Sum squared resid611922.2Schwarz criterion14.60266Log likelihood-5633118Hannan-Quinn criter.14.448

9、85F-statistic1603514Durbin-Watson stat1.720479Prob(F-statistic)0.000015图5J后一个样本的OLS估计结果如图5-2所示。Dependent Variable: YMethod: Least SquaresDate: 12/07/11 Time: 22:26Sample: 1 8In eluded observations: 8VariableCoefficientStd.臼rort-StatisticProb.X0.5541260.3114321.7792870.1255C1277.1611540.6040.8290000.

10、4388R-squared0345397Mean dependent var4016.814SE of regression145.2172Akaike info criterion13.00666Sum squared resid126528.3Schwarz criterion13.02652Log likelihood50.02663HannanQuinn criter.12.87271F-statistic3.165861Durbin-Watson stat3.004532Prob(F-statistic)0.125501图52于是得到如下F统计量:RSSi/(8-l-l) _ 611

11、922.2/6 _4 g4RSS2/(8-l-l) 一 126528.3/6 一 '在5%的显著性水平下，自由度为（6,6 ）的F分布的临界值为F0.05（6r6）=4.28o所以, 拒绝无异方差性假设,表明原模型存在异方差。（2 ）怀巒佥验记e2对原始模型进行普通最小二乘回归得到的残差平方项，将其与x及灯作辅助 回归,得到结果如图5-3所示。Heteroskedasticity Test: Breusch-PaganGodfreyF-statistic14.50681Prob. F(2,l刀0.0002Obs*R-squared12.61088Prob. Chi-Square(2)0

12、.0018Scaled explained SS5.525171Prob. Chi-Square(2)0.0631Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 12/09/11 Time: 19:30Sample: 1 20In eluded observations: 20VariableCoefficientStd. Error t-StatisticProb.C-176606.0102909.4-1.7161300.1043X48.2229128.824291.6729960.1126XA2-0.0

13、020440.001840-1.1110010.2820R-squared0.630544Mean dependent var42163.02Adjusted R-squared0.587079SD dependent var44992.75SE of regression28911.87Akaike info criterion23.51937Sum squared resid1.42E+10Schwarz criterion23.66873Log likelihood-232.1937Hannan-Quinn criter.23.54853F-statistic14.50681Durbin

14、-Watson stat0.982684Prob(F-statistic)0.000211图5-3e2=-176606.0+48.22X-0.002044 X2(-1.716)(1.673)(-1.111)R2 二 0.6305怀特统计量nR2=20x0.6305=12.61该值大于5%显普性水平下、自由度为2的2分布的相应临界值2o.os= 5.99 ,因此r拒绝同方差的原假设。(3)采用加权最小二乘法对原模型进行回归为了寻找适当的权，作In"关于OLS回归，结果如图5-4所示。Dependent Variable: L0G(EA2)Method: Least SquaresDat

15、e: 12/09/11 Time: 20:07Sample: 1 20In eluded observations: 20VariableCoefficientStd.臼ror t-StatisticProb.X0.0004590.0001652.7865100.0122C6.8292971.1285826.0512180.0000R-squared0.301368Mean dependent var9.825601Adjusted R-squared0.262555SD dependent var1.784758SE of regression1.532654Akaike info crit

16、erion3.786518Sum squared resid42.28250Schwarz criterion3.886091Log likelihood-35.86518HannarrQuinn criter.3.805956F-statistic7.764640Durbin-Watson stat2.216470Prob(F-statistic)0.012184图54结果为：Ine2 二 6.829297+0.000459X(6.0512)(2.7865)R2 二 0.3014于是,可生成权序列Wj=1/7(6.829297+0.000459X)。对原模型进行加权最小 二乘估计得到如图5-

17、5所示。Dependent Variable: YMethod: Least SquaresDate: 12/09/11 Time: 20:25Sample: 1 20In eluded observati ons: 20Weighting series: WVariableCoefficie ntStd. Errort-StatisticProb.X0.7402550.03566920.753680.0000C357.8106197.57511.8110100.0869Weighted StatisticsR-squared0.959885Mean dependent var4650.593

18、Adjusted R-squared0.957657SD dependent var881.0317SE of regression171.9364Akaike info criterion13.22677Sum squared resid532118.2Schwarz criterion13.32634Log likelihood-130.2677Hannan-Quinn criter.13.24620F-statistic430.7153Durbin-Watson stat1.556017Prob(F-statistic)0.000000Un weighted StatisticsR-sq

19、uared0.982748Mean dependent var5199.515Adjusted R-squared0.981790SD dependent var1625.275SE of regression2193233Sum squared resid865848.5Durbin-Watson stat1.309635图55对原模型进行加权最小二乘估计(WLS )得到AY =357.81+0.74X(1.811 )( 20.754 )R2二0.9599 D.W.二 1.556F=430.715可以看出,与不加权的OLS相比，加权最小二乘估计使得X前的参数值略有下降，说 明可支配收入对消费

20、支出的影响被略微高估了 ,标准差增大了 ,说明OLS估计低估了 X对 应参数的标准差。下面women检验是否加权的回归模型已不存在异方差性。记经加权的回归模型为wY 邙 ow+SiX+屮该模型的普通最小二乘回归结果为wr =357.81w+0.74wX记该回归模型的残差估计的平方为e2*,将其与w, wx及其平方项作辅助回归，得e2*=-5519.69+19027339w-50471wX-805000000w2-28.998(wX)2(-1.42)(136)(-136)(20.42)R2=0.153怀特统计量nR2=20x0.153=0.306该值小于5%显蕃性水平下、自由度为4的2分 布的相

21、应临界值20.05=9.49 ,因此，不拒绝同方差的原假设。(4)异方差稳健标准误法进行修正异方差稳健标准误法修正的结果如图5-6所示Dependent Variable: YMethod: Least SquaresDate: 12/09/11 Time: 21:19Sample: 1 20In eluded observati ons: 20White Heteroskedasticity-C on sistent Standard Errors & CovarianceVariableCoefficientStd. Error t-StatisticProb.X0.7553680

22、.03159623.907410.0000C271.1197181.54701.4933860.1527R-squared0.983198Mean dependent var5199.515Adjusted R-squared0.982265SD dependent var1625.275SE of regression216.4435Akaike info criterion13.68718Sum squared resid843260.4Schwarz criterion13.78675Log likelihood-134.8718Hannan-Quinn criter.13.70661F

23、-statistic1053.318Durbin-Watson stat1.302512Prob(F-statistic)0.000000图56异方差稳健标准误法修正的结果为A>z=271.12+0.7554X(1.493 )( 23.907 )R2=0.9832 D.W. =1.3025 F=1053.38可以看出，估计的参数与OLS相比较,结果几乎相同，只是改变了标准差，标准差变 大，从而t检验值变小。6 .序列相关性检验(1) D.W.检验法在Eviews软件下,根据图2-2的OLS估计结果，D.W.值为1.3025 ,大于显著性水平 为5%下，样本容呈为20的D.W.分布的下限临界值dL=1.20 ,小于上限临界值du=1.41 , 所以D.W.检验法不能确走该模型是否存在一阶自相关性。(2 )拉格朗日成数检验(LM )检验在Eviews软件下,含1阶滞后残差项的LM检验如图6-1所示。Breusch-Godfrey Serial Correlation LM Test:F-statistic1.097067Prob. F(l,17)03096Obs*R-squared1.212426Prob Chi-Square(l)0.2709Test Equation:Dependent Variable: RESID